Standing Solitary Waves as Transitions to Spiral Structures in Gravitationally Unstable Accretion Disks

Abstract

Astrophysical disks that are sufficiently cold and dense are linearly unstable to the formation of axisymmetric rings as a result of the disk’s gravity. In practice, spiral structures are formed, which may in turn produce bound fragments. We study a nonlinear dynamical path that can explain the development of spirals in a local model of a gaseous disk on the subcritical side of the gravitational instability bifurcation. Axisymmetric equilibria can be radially periodic or localized, in the form of standing solitary waves. The solitary solutions have energy slightly larger than a smooth disk. They are further unstable to nonaxisymmetric perturbations with a wide range of azimuthal wavenumbers. The solitary waves may act as a pathway to spirals and fragmentation.